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As excellent nonlinear optical (NLO) crystals, YCa4O(BO3)3 (YCOB) and GdCa4O(BO3)3 (GdCOB) have been paid much attention since their first appearance in 1990’s. From that time to now, almost all of related researches and applications have focused on their type-I phase-matching (PM) configurations which possess large effective NLO coefficient (deff). In this paper, type-II second-harmonic-generation (SHG) properties of these two crystals are reported, including PM curve, deff, angular acceptance and walk-off angle. Both of the type-II SHG experiments for 1064 and 1320 nm have indicated that the optimum directions which have maximum deff locate in the second octant, i.e. (90° < θ< 180°, 0° < ϕ < 90°). For a (112°, 81.3°)-cut, 24 mm long YCOB crystal, the largest type-II SHG conversion efficiency of a 1064 nm Nd:YAG pico-second laser is 55%, which reaches the same level of the optimum type-I sample. To our knowledge this is the first time that type-II SHG performance of YCOB and GdCOB crystals is investigated intensively. Our research has shown that the smaller deff of type-II PM can be compensated by its larger angular acceptance and less beam walk-off. The same level SHG conversion efficiency implies for such type crystals the type-II components have the potential to replace type-I ones and obtain important NLO applications in the future.
© 2015 Optical Society of America
1. Introduction
Up to now, many famous NLO crystals such as KH2PO4 (KDP), KD2PO4 (DKDP), KTiOPO4 (KTP), BiB3O6 (BIBO), BaB2O4 (BBO), LiB3O5 (LBO) and KBe2BO3F2 (KBBF) etc. have been used for frequency conversion to obtain high-power visible or ultraviolet (UV) lights, which have been applied in many important fields including precise material processing, laser marking, disc mastering, optical data storage, laser printing and spectroscopy etc [1–3]. In the past two decades, monoclinic rare-earth calcium oxyborate crystals ReCa4O(BO3)3 (ReCOB, Re = Y and Gd) were investigated widely due to their many merits, including good thermal properties, wide optical transparency, large nonlinearity, and stable physical and chemical characteristics [4, 5]. Particular important is these crystals show neglectable hygroscopy and can be readily grown into large size by the conventional Czochralski (Cz) method. Large YCOB crystals with 4 inches in diameter and 4 inches in length have been achieved in lab, and reported to be a good candidate for optical parametric chirped-pulse amplification (OPCPA) systems [6–9]. Yb3+ doped ReCOB crystals were reported to be excellent laser host materials for ultrafast laser, and 35 femtosecond mode-locked pulses have been achieved in Yb:YCOB crystal [10, 11]. For self-frequency doubling (SFD) application, more than 3 watts 545 nm green laser was obtained with Nd:GdCOB crystal [12]. In addition, the refrective index of GdxY1-xCa4O(BO3)3 (GdxY1-xCOB) crystals could be adjusted continiously by changing the compositional parameter x during crystal growth, and noncritical phase matching (NCPM) SHG as well as third harmonic generation (THG) of Nd:YAG laser (1064 nm) could be realized along their two fold principal axis, i.e. Y optical principal direction [13]. In summary, ReCOB and their derivatives have been recognized as excellent NLO and laser materials, and have gained a series of exciting achievements in many scopes.
Nevertheless, for NLO applications of ReCOB crystals, almost all of the reports by time now have been focused on the type-I PM styles [13–26], which might be attributed to their larger nonlinearity than that of type-II PM configurations. The only discussions about type-II PM are very limited and discrete [4, 14, 20, 23, 25]. In fact, comparing with type-I PM, type-II frequency conversion of NLO crystal possess many special advantages such as large angular acceptance and small beam walk-off [27, 28]. Beside of nonlinearity, these parameters are also pivotal factors for stable, large energy and high efficiency frequency conversion [29–31]. Moreover, the second-order NLO coefficient tensor (dij) measured by type-I SHG was suggested to be verified by type-II SHG experiments [20, 22], and the dij could be determined more accurately in this way. So a focused research on type-II PM of YCOB and GdCOB crystals have special important values, for the exploration of basic property, and also for the diversity of design scheme in practical applications.
In this paper, firstly we theoretically calculate the type-II PM SHG attributes for YCOB and GdCOB crystals, including PM angle, deff, angular acceptance and walk-off angle. Then the spatial distribution of deff is examined by the SHG experiments of pico-second Nd:YAG and optical parametric oscillation (OPO) laser sources. In this way, the optimum directions for type-II SHG which have maximum deff are determined, and at the same time the sign of the key nonlinear coefficient d31 is identified to be negative. At last, an efficient type-II SHG experiment is performed by a pico-second Nd:YAG laser, and the optimum type-II sample exhibit the same level conversion efficiency as the optimum type-I sample dose, which lights up a bright torch for type-II PM applications of such type crystals.
2. Calculations
The PM direction k is expressed in the form of (θ, ϕ), where θ is the angle between k and the Z axis, and ϕ is the angle between the XY-plane projection of k and the X axis. For monoclinic crystals such as ReCOB, the two-fold axis b is always parallel to the Y axis but with a reverse direction. This implies that the direction (θ, ϕ) is equivalent to the direction (180-θ, 180-ϕ). As two important output wavelengths of Nd3+ solid state laser, 1064 and 1320 nm are selected as the fundamental light to perform the followed calculations. Based on the Sellmeier equations of YCOB and GdCOB crystals reported by Umemura et al. [21], both of type-I and type-II SHG PM directions in the whole space were calculated for YCOB and GdCOB crystals, as shown in Fig. 1. The calculated results also indicate that the type-II PM at 1064 nm is not available for GdCOB crystals, which is associated with its relative small birefringence [24]. However, both of YCOB and GdCOB crystals can satisfy the conditions for the type-II SHG at 1320 nm. Among the numerous type-II PM directions of YCOB and GdCOB crystals, the PM directions in the principal planes are attractive for the easy of processing crystal samples and high rate of utilization the as-grown crystals, furthermore, related second order NLO coefficients dij can be determined by SHG experiments [22]. For YCOB crystals, the 1064 nm type-II PM directions in the YZ and XY principal planes are (62.8°, 90°) and (90°, 75.4°), and the 1320 nm type-II PM directions in the XZ and XY principal planes are (12.5°, 0°) and (90°, 53.2°), respectively. The 1320 nm type-II PM directions of GdCOB crystals in the YZ and XY principal planes are (51.7°, 90°) and (90°, 70°), respectively.
Referring to the NLO coefficients dij of YCOB and GdCOB crystals [20], the |deff| on the whole PM directions for YCOB and GdCOB crystals at 1064 and 1320 nm are calculated, as shown in Fig. 2 (red line). It can be seen that the type-I and type-II optimum PM directions which have maximum |deff| for these two crystals are all in the second octant, i.e. (90° < θ < 180°, 0° < ϕ < 90°). Concretely speaking, combining Fig. 1 with Fig. 2 it can be determined that for type-I and type II SHG of 1064 nm, they are (113°, 37.1°), (112°, 81.3°) in YCOB crystal. For type-I and type II SHG of 1320 nm, they are (113°, 28.7°), (138°, 55.4°) in YCOB crystal, and (113°, 36.1°), (120°, 77.3°) in GdCOB crystal, respectively. All of these directions are special spatial configurations which are not in principle planes.
Fig. 2 Calculation results of |deff|. Red lines come from the NLO tensors of Pack et al where d31 is negative [20], blue lines assume that the sign of d31 is positive, and θi (i = 1-10) are type-II PM directions selected for examining the distribution of |deff|.
By the time, a number of papers have reported the NLO coefficients of YCOB and GdCOB crystals, which were measured by frequency doubling of 1064 nm [20, 22, 25, 26], or calculated with molecular orbital theory [19, 32]. Only Pack and Wang presented all of the NLO coefficients of these two crystals [20, 22]. The results of Wang et al. were come from a combination of anion group theory, CNDO approximation and pico-second high efficiency SHG experiments, which seemed obviously larger than Pack’s, so a 0.73 times modification was suggested by the latter. The results of Pack et al. were obtained by the separated-beams method, which permitted straightforward measurement of the entire nonlinear tensor, including the relative signs of the coefficients. Beside of the magnitude, the largest difference between these two set of values is the sign symbol of d31 is different, so does the other author’s values [22, 25, 26, 32]. For type-I frequency doubling, they provided nearly the same |deff| spatial distribution and the maximum |deff| direction, however, they made distinctly different predictions on the |deff| spatial distribution for type-II SHG [20]. Assuming the sign of d31 of Pack’s tensor is positive, we could obtain new |deff| spatial distributions, as shown in Fig. 2 (blue line). Compared with red lines, it can be seen that the magnitude and distribution of |deff| for type-I SHG are not changed basically, but there are distinct differences for type-II SHG. For the condition of positive d31, the maximum |deff| for type-II SHG in both of YCOB and GdCOB crystals occur at the first octant (0° < θ < 90°, 0° < ϕ < 90°), i.e. (80°, 76.4°) at 1064 nm in YCOB, (84°, 53.3°) at 1320 nm in YCOB, and (80°, 70.7°) at 1320 nm in GdCOB, respectively. The controversial conclusions between red lines and blue lines can be examined by type-II SHG experiments, which will be introduced in the next part. At the same time, it also manifest that the sign symbol of d31 is very important for determining the type-II frequency conversion properties of such crystals.
The angular acceptance and walk-off angle are also two important parameters for NLO frequency conversion, beside of the deff. Based on the Sellmeier equations of YCOB and GdCOB crystals [21], and supposing the crystal length was 10 mm, these properties were calculated for the whole SHG PM configurations at 1064 and 1320 nm, as shown in Fig. 3. It could be seen that in most cases type-II PM exhibits much better data than type-I PM does, i.e. larger angular acceptance (~2-5 times) and smaller walk-off angle (~0.25-1 times).
3. Type-II SHG experiments
3.1 SHG conversion at 1064 nm
In this experiment, YCOB samples with unified dimensions of 4 × 4 × 8 mm3 were processed along different PM directions, including (62.8°, 90°), (80°, 76.4°), (90°, 75.4°) and (112°, 81.3°). In the following part, they are defined as θ1 to θ4, as shown in Fig. 2(b). The laser source was a PY61 Nd:YAG pico-second laser made by Continuum Corp. USA. The work wavelength, repeat frequency and pulse width were 1064 nm, 10 Hz and 40 ps, respectively. In order to optimize the incident laser beam, a diaphragm (ϕ = 3 mm) was set before the crystal sample. The filter placed between crystal and energy meter transmit 0.4% at 1064 nm and 80% at 532 nm. The SHG output energy and conversion efficiency with the change of fundamental density are shown in Fig. 4. It can be seen that the highest conversion efficiency come from the θ4 sample, which reaches 22.4% at a fundamental intensity of 1.36 GW/cm2. For the red line of Fig. 2(b), there is |deff (θ4)| > |deff (θ1)| > |deff (θ3)| > |deff (θ2)|. While for the blue line of Fig. 2(b), there is |deff (θ2)| > |deff (θ3)| > |deff (θ1)| > |deff (θ4)|, and it takes on a completely reverse order with the red line. Since the SHG output energy and conversion efficiency will correspond to the magnitude of |deff| if the crystal length is kept the same, from Fig. 4 we can conclude that the |deff| distribution plotted with red line in Fig. 2(b) is correct.
3.2 SHG conversion at 1320 nm
For the 1320 nm SHG experiments, an OPO (Opolette HE 355 II) tunable laser was used as the pump source (410~2400 nm). The output light was linearly polarized along the vertical direction. The laser pulse width was about 5 ns and the repetition rate was 20 Hz. The average output power depended on the work wavelength, which was tunable in the range of 2-12 mW. In order to increase the intensity of fundamental laser, the beam was focused by a long focal length lens (ƒ = 360 mm). The fundamental and SHG waves were separated by a filter, and then measured by a power meter. For YCOB crystals, the samples with dimensions of 4 × 4 × 6 mm3 were cut along (84°, 53.3°), (90°, 53.2°) and (138°, 55.4°) PM directions. In the following part, they are defined as θ5, θ6, and θ7, as shown in Fig. 2(d). Their SHG output power and conversion efficiency at 1320 nm were shown in Fig. 5. For the red line of Fig. 2(d), there is |deff (θ7)| > |deff (θ5)| > |deff (θ6)|. For the blue line of Fig. 2(d), there is |deff (θ5)| > |deff (θ6)| > |deff (θ7)|. From Fig. 5 we can see that the |deff| distribution plotted with red line in Fig. 2(d) is correct, and the θ7 sample exhibits the best SHG results.
The GdCOB samples with dimensions of 4 × 4 × 6 mm3 were cut along (80°, 70.7°), (90°, 70°) and (120°, 77.3°) PM directions for the 1320 nm SHG experiments. In the following part, they are defined as θ8, θ9, and θ10, as shown in Fig. 2(f). Their SHG output power and conversion efficiency were shown in Fig. 6. Because of the low power and poor beam quality of the fundamental laser, the SHG output power and conversion efficiency were very low at OPO experimental conditions, but it was easy to distinguish the SHG effects of different samples. Under the same fundamental intensity, the SHG output energy and conversion efficiency of θ10 were obviously larger than those of θ8 and θ9 samples. For the red line of Fig. 2(f), there is |deff (θ10)| > |deff (θ9)| > |deff (θ8)|. For the blue line of Fig. 2(f), there is |deff (θ8)| > |deff (θ9)| > |deff (θ10)|. From Fig. 6 we can see that the |deff| distribution plotted with red line in Fig. 2(f) is correct.
4. Discussions and applications
Based on the above experimental results, the maximum |deff| of type-II SHG for both of YCOB and GdCOB crystals appear at the second not the first octant in spatial directions, so the |deff| distributions described by red lines in Fig. 2 are correct. It means that the sign symbol of d31 is negative, and such property can only be determined by type-II PM experiments. In some previously literatures such as reference [19] and its influenced reference [22], the sign symbol of d31 is assumed to be positive, which could not be tested before because most researches concentrated on type-I PM. As shown in Fig. 2, the sign of d31 does not affect type-I PM properties basically, but become crucial when type-II PM is concerned. The present research gives out a conclusion of this question.
The 1064 and 1320 nm type-II SHG optimum PM directions for YCOB crystal were found to be (112°, 81.3°) and (138°, 55.4°), respectively, and the 1320 nm type-II SHG optimum PM direction for GdCOB crystal was determined to be (120°, 77.3°). The type-II and type-I SHG properties including the PM angles, |deff|, angular acceptance and walk off angle at 1064 and 1320 nm were summarized in Table 1. For type-II SHG, although its deff are obviously smaller than that of type-I SHG, it still exhibits eye-catching advantages in angular acceptance and beam walk-off. For example, for 1064 nm SHG of YCOB crystal, the optimum type-II and type-I PM angles which have largest |deff| are (112°, 81.3°) and (113°, 37.1°), respectively, as shown in Table 1. Although the |deff| of (112°, 81.3°) direction is only 0.32 pm/V, the acceptance angle and walk-off angle of this direction are 6.8 and 5.1 mrad, which are 9.7 and 0.26 times of the corresponding data for (113°, 37.1°) direction, respectively. The large angular acceptance and small beam walk-off of type-II PM will help to increase SHG output power and conversion efficiency by using of long crystal, and benefit related frequency conversion, as well as SFD application.
Table 1. The SHG properties of some representative PM directions in YCOB and GdCOB crystals
In order to further confirm the practicability of type-II PM, three (112°, 81.3°)-cut YCOB crystal samples with different lengths (8, 16 and 24 mm) were prepared for the high efficiency SHG experiment of 1064 nm, with the PY61 Nd:YAG pico-second laser as the fundamental light source. Three type-I PM (113°, 37.1°)-cut YCOB crystals with lengths of 8, 12 and 16 mm were served as the references. Figure 7 gave the variation of the SHG conversion efficiency as a function of fundamental intensity for different samples, which was measured at room temperature. As the optimum type-II PM configuration which has the largest |deff| (0.32 pm/V), (112°, 81.3°)-cut sample took on better SHG output when the crystal length increased. The highest SHG conversion efficiency of the 24 mm sample reached 55%, which is obviously superior to the data of 8 mm (26.5%) and 16 mm (47.2%) samples at the same fundamental intensity of 1.65 GW/cm2. At the same time, this value is a little better than the 52% or so efficiency of the (113°, 37.1°) samples with different lengths of 8, 12 and 16 mm, which is the optimum type-I PM direction that has the largest |deff| (1.42 pm/V). As shown in Fig. 7, for each type of PM configuration (type-I or type-II), longer YCOB crystal can generate higher SHG output and efficiency at low fundamental intensity. Meanwhile, owing to the much larger |deff|, the type-I PM samples are more liable to be saturated, and at low fundamental intensity exhibit rapider increasing of SHG efficiency than the type-II PM samples do on the whole. Nevertheless, because of the small angular acceptance and large walk-off angle, the optimum crystal length is relatively small, which is ~8 mm under the present experimental conditions. On the contrary, type-II PM of YCOB possesses better angular acceptance and smaller beam walk-off, so its optimum crystal length has substantially increased (> 24 mm), the disadvantage of small |deff| is compensated and the ultimate SHG conversion efficiency can reach the same level as the optimum type-I PM.
5. Conclusion
Based on the calculation and SHG experiments, we find that the maximum |deff| of type-II SHG for both of YCOB and GdCOB crystals occur at the second not the first octant in spatial direction, which is associated with the negative sign symbol of d31. For the first time, the type-II SHG properties including the PM curves, |deff|, angular acceptance and walk off angle of these two crystals were investigated systematically. The 1064 and 1320 nm type-II SHG optimum PM directions for YCOB crystal were found to be (112°, 81.3°) and (138°, 55.4°), respectively, and the 1320 nm type-II SHG optimum PM direction for GdCOB crystal was determined to be (120°, 77.3°). For type-II PM styles, although its |deff| is much smaller than type-I PM, yet this shortcoming can be compensated by other advantages, such as large angular acceptance and low beam walk-off. By increasing the interaction length of type-II PM sample, we have obtained the same level SHG conversion as type-I PM. This fact illustrates for such crystals type-II PM configurations also have great application potentials in NLO domain.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61178060, 51202129 and 91022034), Nature Science Foundation of Shandong Province (ZR2012EMQ004), and Natural Science Foundation for Distinguished Young Scholar of Shandong Province (2012JQ18).
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